Why doesn't Bendy Bones' Easing property work in pose mode?
Well it kind of works, as you can see in this Blend File here:



I say kind of because the limitation is that you have to set up the driver which he's using in the video. Looks like a dependency graph issue to me to be honest. This theory is backed up by two things:


if you transform the controller bone, and cancel that transform using Esc the bendy bone does not jump back into its original state (that's a bad bad thing)
if you run Blender from the command line using the  --enable-new-depsgraph switch, everything works totally fine, even not having drivers on the bone deforms the mesh as it should.


You could try having the controller bone in a separate armature object. That might help overcoming the dependency graph issue. Or simply run Blender with new depsgraph on as indicated before.